Banach Spaces: Volume 1
North-Holland (Publisher)
Published on 30. April 2001
Book
Hardback
400 pages
978-0-444-50749-5 (ISBN)
More details
Series
Language
English
Place of publication
United States
Publishing group
Elsevier Science & Technology
Target group
Professional and scholarly
Product notice
Laminated cover
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 24 mm
Weight
735 gr
ISBN-13
978-0-444-50749-5 (9780444507495)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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Content
Introduction.
Some Notation and Terminology.
1. Banach Spaces.
1.1 Normed Spaces.
1.1.1 General Results.
1.1.2 Some Standard Examples.
1.1.3 Minkowski's Theorem.
1.1.4 Locally Compact Normed Spaces.
1.1.5 Products of Normed Spaces.
1.1.6 Summable Families.
Exercises.
1.2 Operators.
1.2.1 General Results.
1.2.2 Standard Examples.
1.2.3 Infinite Matrices.
1.2.4 Quotient Spaces.
1.2.5 Complemented Subspaces.
1.2.6 The Topology of Pointwise Convergence.
1.2.7 Convex Sets.
1.2.8 The Alaoglu-Bourbaki Theorem.
1.2.9 Bilinear Maps.
Exercises.
1.3 The Hahn-Banach Theorem.
1.3.1 The Banach Theorem.
1.3.2 Examples in Measure Theory.
1.3.3 The Hahn-Banach Theorem.
1.3.4 The Transpose of an Operator.
1.3.5 Polar Sets.
1.3.6 The Bidual.
1.3.7 The Krein-Smulian Theorem.
1.3.8 Reflexive Spaces.
1.3.9 Completion of Normed Spaces.
1.3.10 Analytic Functions.
Exercises.
1.4 Applications of Baire's Theorem.
1.4.1 The Banach-Steinhaus Theorem.
1.4.2 Open Mapping Principle.
Exercises.
1.5 Banach Categories.
1.5.1 Definitions.
1.5.2 Functors.
1.6 Nuclear Maps.
1.6.1 General Results.
1.6.2 Examples.
1.7 Ordered Banach Spaces.
1.7.1 Ordered Normed Spaces.
1.7.2 Order Continuity.
Name Index. Subject Index. Symbol Index.
Some Notation and Terminology.
1. Banach Spaces.
1.1 Normed Spaces.
1.1.1 General Results.
1.1.2 Some Standard Examples.
1.1.3 Minkowski's Theorem.
1.1.4 Locally Compact Normed Spaces.
1.1.5 Products of Normed Spaces.
1.1.6 Summable Families.
Exercises.
1.2 Operators.
1.2.1 General Results.
1.2.2 Standard Examples.
1.2.3 Infinite Matrices.
1.2.4 Quotient Spaces.
1.2.5 Complemented Subspaces.
1.2.6 The Topology of Pointwise Convergence.
1.2.7 Convex Sets.
1.2.8 The Alaoglu-Bourbaki Theorem.
1.2.9 Bilinear Maps.
Exercises.
1.3 The Hahn-Banach Theorem.
1.3.1 The Banach Theorem.
1.3.2 Examples in Measure Theory.
1.3.3 The Hahn-Banach Theorem.
1.3.4 The Transpose of an Operator.
1.3.5 Polar Sets.
1.3.6 The Bidual.
1.3.7 The Krein-Smulian Theorem.
1.3.8 Reflexive Spaces.
1.3.9 Completion of Normed Spaces.
1.3.10 Analytic Functions.
Exercises.
1.4 Applications of Baire's Theorem.
1.4.1 The Banach-Steinhaus Theorem.
1.4.2 Open Mapping Principle.
Exercises.
1.5 Banach Categories.
1.5.1 Definitions.
1.5.2 Functors.
1.6 Nuclear Maps.
1.6.1 General Results.
1.6.2 Examples.
1.7 Ordered Banach Spaces.
1.7.1 Ordered Normed Spaces.
1.7.2 Order Continuity.
Name Index. Subject Index. Symbol Index.